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This is a very ancient tradition, proven to have existed in Rome since the fourth century. On it we give thanks to God for the mission he entrusted to the Apostle Peter and his Successors.
“Cathedra” literally means the established seat of the Bishop, placed in the mother church of a diocese which for this reason is known as a “cathedral;” it is the symbol of the Bishop’s authority and in particular, of his “magisterium", that is, the evangelical teaching which, as a successor of the Apostles, he is called to safeguard and to transmit to the Christian Community. ...
The See of Rome, after St. Peter’s travels, thus came to be recognized as the See of the Successor of Peter, and its Bishop’s “cathedra” represented the mission entrusted to him by Christ to tend his entire flock. ...
Celebrating the “Chair” of Peter, therefore, as we are doing today, means attributing a strong spiritual significance to it and recognizing it as a privileged sign of the love of God, the eternal Good Shepherd, who wanted to gather his whole Church and lead her on the path of salvation [General Audience, Feb. 22, 2006].